Question

A force F=6i-8j+10k newton produces acceleration 1m/s2 in a body. The mass of the body is in kg

Answer 1

F = 6i - 8j + 10k
F = sqrt(6^2 + 8^2 + 10^2)
F = 14.14 N

m = F/a
= 14.14 / 1
= 14.14 kg

Mass of body is 14.14 kg

Answer 2

The mass of the body is 14.14 kg

Given:

$F = 6i - 8j + 10k$

Acceleration = 1 $m/s^2$

Solution:

We can calculate the magnitude of the given vector.

$F=\sqrt{6^{2}+8^{2}+10^{2}}$

$F=\sqrt{36+64+100}$

$\Rightarrow F=\sqrt{200}$

$\Rightarrow F=14.14 \ N$

By Newton’s second law of motion,

$F= \text{Mass} \times \text{Acceleration}$

Since, we need to determine the mass, we need to rearrange, we get,

$\Rightarrow m=\frac{F}{a}$

Therefore, by substituting the values in this equation, we get.

$m=\frac{14.14}{1}$

$m=14.14 \ \mathrm{kg}$